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# Tag Archives: association scheme

## Proper Jordan schemes exist!

A new field of research has just been created by Misha Klin, Misha Muzychuk and Sven Reichard: proper Jordan schemes. They answered a question which I posed some time ago (I don’t remember when), about whether such objects exist. I … Continue reading

## Association schemes for diagonal groups

Sean Eberhard commented on my posts on diagonal groups (see here and here). He is correct; there is an association scheme preserved by the full diagonal group with n factors in the socle; it is non-trivial if n > 2. The details … Continue reading

Posted in open problems
Tagged association scheme, diagonal group, Latin hypercube, Latin square
1 Comment

## A problem

Since I have been saying rather a lot about association schemes and coherent configurations lately, I thought I would mention an open problem. This is probably one for the experts, and I guess it has been ignored because of the … Continue reading

Posted in open problems
Tagged association scheme, coherent configuration, permutation group
8 Comments

## Synchronization and all that, 2

The story I told in the last post is not over. The recent development is that we spotted a mistake in the paper. An easy mistake to make: we had simply used the symbol n in two different places with … Continue reading

Posted in doing mathematics, exposition
Tagged association scheme, large sets, ovoid, Philippe Delsarte, quadric, spread, Steiner systems, synchronization, triality
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## Synchronization and separation in the Johnson schemes

Today a paper by Mohammed Aljohani, John Bamberg and me went on the arXiv on this topic. Here is a brief summary of what it is about. Synchronization comes in several flavours, and the point of the paper is to … Continue reading

Posted in exposition, Uncategorized
Tagged association scheme, Peter Keevash, Philippe Delsarte, separation, synchronization
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## More graphs

John Bamberg is reporting on New Directions in Combinatorics on SymOmega (his report on Day 1 is here), so I will not even attempt to be comprehensive, but will just pick some plums. Not very long ago, I reported the … Continue reading

Posted in events, exposition, history
Tagged association scheme, characters, Graham Higman, Moore graph, partial difference set, Stefaan De Winter
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## Terminology: association scheme or coherent configuration?

At the Villanova conference, many of the talks were about association schemes or coherent configurations, or indeed generalisations of these. A certain tension between different uses of these terms was evident. I’d like to set down my own views here. … Continue reading

Posted in exposition, history
Tagged association scheme, Bose, coherent configuration, Higman, Leman, Mesner, Nair, Schur ring, Shimamoto, Terwilliger, Weisfeiler
2 Comments

## Multiply transitive permutation sets

Bill Fahle asked, in a comment on the preceding post, for information about sets of permutations which are multiply transitive (but not necessarily groups or sharply multiply transitive). I take “t-transitive set” to mean a set S of permutations of … Continue reading

## Coherent configurations and all that, 1

I’m off to Lisbon next week for three weeks. Among other things, I will be giving four lectures at the Centre for Algebra at the University of Lisbon. One of these will touch on aspects of association schemes and coherent … Continue reading